In other words, why should I learn about it? When am I going to say... oh I need to know about push down automata or turing machines for this.
I am not able to see the applications of the material. Thanks
You should learn about automata theory because it will help you understand what is computationally possible in a given system. People who understand the difference between a push-down automata and a universal turing machine understand why trying to parse HTML with regular expressions is a bad idea. People who don't think it is just fine to try to parse HTML with REs.
There are problems that are nice fit to this kind of solutions, some of which are:
There are probably many others. If you start writing code that has some ad-hoc state variable depending on which some functions can do this or that, you can probably benefit from proper FSA.
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